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%TCIDATA{Created=Thu Mar 25 16:19:17 2004}
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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}

\begin{document}
Al simplificar $\left(  \dfrac{x^{-1/2}}{y^{2/5}}\right)  ^{-4}\left(
\dfrac{3y^{-4/5}}{2x^{2}}\right)  ^{4}$ hasta llegar a la m\'{\i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{81}{16x^{6}\left(
\sqrt[5]{y}\right)  ^{8}}\qquad$b) $\dfrac{81}{16x^{3}\left(  \sqrt[5]%
{y}\right)  ^{8}}\qquad$c) $\dfrac{81}{8x^{6}\left(  \sqrt[5]{y}\right)  ^{8}%
}\qquad$d) $\dfrac{81}{16x^{6}\left(  \sqrt[3]{y}\right)  ^{8}}$

Al simplificar $\left(  \dfrac{2x^{-1/2}}{y^{2/5}}\right)  ^{-4}\left(
\dfrac{3y^{-4}}{x^{2}}\right)  ^{4}$ hasta llegar a la m\'{\i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{81}{16x^{6}\left(
\sqrt[5]{y}\right)  ^{72}}\qquad$b) $\dfrac{81}{16x^{6}\left(  \sqrt[5]%
{y}\right)  ^{68}}\qquad$c) $\dfrac{81}{16x^{4}\left(  \sqrt[5]{y}\right)
^{68}}\qquad$d) $\dfrac{81}{16x^{6}\left(  \sqrt[3]{y}\right)  ^{72}}$

Al simplificar $\left(  \dfrac{5x^{-1/2}}{y^{2/5}}\right)  ^{-4}\left(
\dfrac{10y^{-4/2}}{x^{2/5}}\right)  ^{4}$ hasta llegar a la m\'{\i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $16\dfrac{\left(  \sqrt[5]%
{x}\right)  ^{2}}{\left(  \sqrt[5]{y}\right)  ^{32}}\qquad$b) $16\dfrac
{\left(  \sqrt[5]{x}\right)  ^{4}}{\left(  \sqrt[5]{y}\right)  ^{32}}\qquad$c)
$16\dfrac{\left(  \sqrt[5]{x}\right)  ^{2}}{\left(  \sqrt[5]{y}\right)  ^{16}%
}\qquad$d) $8\dfrac{\left(  \sqrt[5]{x}\right)  ^{2}}{\left(  \sqrt[5]%
{y}\right)  ^{32}}$

Al simplificar $\left(  \dfrac{3x^{-1/2}}{y^{2}}\right)  ^{-4}\left(
\dfrac{2y^{-4/2}}{x^{2/5}}\right)  ^{4}$ hasta llegar a la m\'{\i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{16}{81}\left(  \sqrt[5]%
{x}\right)  ^{2}\qquad$b) $\dfrac{16}{81}\left(  \sqrt[5]{x}\right)  ^{2}%
y^{2}\qquad$c) $\dfrac{7}{6}\left(  \sqrt[5]{x}\right)  ^{2}\qquad$d)
$\dfrac{16}{81}\left(  \sqrt[5]{x}\right)  ^{4}$

Al simplificar $\left(  \dfrac{3x^{-1/2}}{3y^{2}}\right)  ^{-2}\left(
\dfrac{y^{-1/2}}{x^{3/2}}\right)  ^{2}$ hasta llegar a la m\'{\i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{1}{x^{2}}y^{3}\qquad$b)
$\dfrac{1}{x^{3}}y^{6}\qquad$c) $\dfrac{1}{x^{4}}y^{3}\qquad$d) $\dfrac
{1}{x^{2}}y^{4}$

Al simplificar $\left(  \dfrac{x^{-1/4}}{5y^{2/3}}\right)  ^{-4}\left(
\dfrac{y^{-3}}{2x^{2}}\right)  ^{4}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{625}{16x^{7}\left(
\sqrt[3]{y}\right)  ^{68}}$\qquad b) $\dfrac{625}{16x^{7}\left(  \sqrt[5]%
{y}\right)  ^{66}}$\qquad c) $\dfrac{625}{16x^{5}\left(  \sqrt[3]{y}\right)
^{68}}$\qquad d) $\dfrac{625}{16x^{5}\left(  \sqrt[5]{y}\right)  ^{66}}$

Al simplificar $\left(  \dfrac{x^{-1/2}}{2y^{1/5}}\right)  ^{-4}\left(
\dfrac{3y^{-2}}{x^{3}}\right)  ^{4}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{1296}{x^{10}\left(
\sqrt[5]{y}\right)  ^{36}}$\qquad b) $\dfrac{1296}{x^{8}\left(  \sqrt[5]%
{y}\right)  ^{34}}$\qquad c) $\dfrac{1296}{x^{10}\left(  \sqrt[3]{y}\right)
^{36}}$\qquad d) $\dfrac{1296}{x^{8}\left(  \sqrt[3]{y}\right)  ^{34}}$

Al simplificar $\left(  \dfrac{x^{-1/3}}{3y^{1/2}}\right)  ^{-3}\left(
\dfrac{2y^{-4}}{2x}\right)  ^{3}$ hasta llegar a la m\'{i}nima expresi\'{o}n
se obtiene:\newline \qquad a) $\dfrac{27}{x^{2}\left(  \sqrt{y}\right)  ^{21}%
}$\qquad b) $\dfrac{27}{x\left(  \sqrt[4]{y}\right)  ^{23}}$\qquad c)
$\dfrac{27}{x\left(  \sqrt[4]{y}\right)  ^{21}}$\qquad d) $\dfrac{27}%
{x^{2}\left(  \sqrt{y}\right)  ^{23}}$

Al simplificar $\left(  \dfrac{x^{-1/4}}{y^{1/7}}\right)  ^{-4}\left(
\dfrac{2y^{-2}}{3x^{3}}\right)  ^{4}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{16}{81x^{11}\left(
\sqrt[7]{y}\right)  ^{52}}$\qquad b) $\dfrac{16}{81x^{9}\left(  \sqrt[3]%
{y}\right)  ^{52}}$\qquad c) $\dfrac{16}{81x^{11}\left(  \sqrt[3]{y}\right)
^{50}}$\qquad d) $\dfrac{16}{81x^{9}\left(  \sqrt[7]{y}\right)  ^{50}}$

Al simplificar $\left(  \dfrac{x^{-1/2}}{y^{1/7}}\right)  ^{-2}\left(
\dfrac{3y^{-3}}{2x^{2}}\right)  ^{2}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{225}{4x^{3}\left(
\sqrt[5]{y}\right)  ^{26}}$\qquad b) $\dfrac{225}{4x\left(  \sqrt[5]%
{y}\right)  ^{23}}$\qquad c) $\dfrac{225}{4x^{3}\left(  \sqrt[3]{y}\right)
^{23}}$\qquad d) $\dfrac{225}{4x\left(  \sqrt[3]{y}\right)  ^{26}}$

Al simplificar $\left(  \dfrac{3x^{-1/3}}{4y^{1/5}}\right)  ^{-3}\left(
\dfrac{2y^{-2}}{x^{3}}\right)  ^{3}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{512}{27x^{8}\left(
\sqrt[5]{y}\right)  ^{27}}$\qquad b) $\dfrac{512}{27x^{6}\left(  \sqrt[5]%
{y}\right)  ^{23}}$\qquad c) $\dfrac{512}{27x^{6}\left(  \sqrt[3]{y}\right)
^{27}}$\qquad d) $\dfrac{512}{27x^{8}\left(  \sqrt[3]{y}\right)  ^{23}}$

Al simplificar $\left(  \dfrac{x^{-1/4}}{4y^{2/3}}\right)  ^{-4}\left(
\dfrac{y^{-3}}{2x^{2}}\right)  ^{4}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{16}{x^{7}\left(
\sqrt[3]{y}\right)  ^{28}}$\qquad b) $\dfrac{16}{x^{5}\left(  \sqrt{y}\right)
^{28}}$\qquad c) $\dfrac{16}{x^{7}\left(  \sqrt[3]{y}\right)  ^{26}}$\qquad
d)$\dfrac{16}{x^{5}\left(  \sqrt{y}\right)  ^{26}}$

Al simplificar $\left(  \dfrac{5x^{-1/2}}{y^{1/3}}\right)  ^{-2}\left(
\dfrac{3y^{-2}}{x}\right)  ^{2}$ hasta llegar a la m\'{i}nima expresi\'{o}n se
obtiene:\newline \qquad a) $\dfrac{9}{25x\left(  \sqrt[3]{y}\right)  ^{10}}%
$\qquad b) $\dfrac{9}{25x\left(  \sqrt{y}\right)  ^{10}}$\qquad c) $\dfrac
{9}{25x^{2}\left(  \sqrt[3]{y}\right)  ^{8}}$\qquad d) $\dfrac{9}{25x\left(
\sqrt[3]{y}\right)  ^{8}}$

Al simplificar $\left(  \dfrac{3x^{-1/3}}{y^{1/4}}\right)  ^{-3}\left(
\dfrac{4y^{-3}}{x^{2}}\right)  ^{3}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{64}{27x^{5}\left(
\sqrt[4]{y}\right)  ^{33}}$\qquad b) $\dfrac{64}{27x^{2}\left(  \sqrt[4]%
{y}\right)  ^{30}}$\qquad c) $\dfrac{64}{27x^{5}\left(  \sqrt[2]{y}\right)
^{33}}$\qquad d) $\dfrac{64}{27x^{5}\left(  \sqrt[4]{y}\right)  ^{31}}$

Al simplificar $\left(  \dfrac{x^{-1/4}}{2y^{1/3}}\right)  ^{-4}\left(
\dfrac{y^{-3}}{3x^{2}}\right)  ^{4}$ hasta llegar a la m\'{i}nima
expresi\'{o}n se obtiene:\newline \qquad a) $\dfrac{16}{81x^{7}\left(
\sqrt[3]{y}\right)  ^{32}}$\qquad b) $\dfrac{16}{81x^{7}\left(  \sqrt
{y}\right)  ^{31}}$\qquad c) $\dfrac{16}{81x^{7}\left(  \sqrt[3]{y}\right)
^{29}}$\qquad d)$\dfrac{16}{81x^{5}\left(  \sqrt[3]{y}\right)  ^{32}}$
\end{document}